7.5 Dictionarybased Coding

1
7.5 Dictionary-based Coding

• LZW uses fixed-length code words to represent
  variable-length strings of symbols/characters
  that commonly occur together, e.g., words in
  English text
• LZW encoder and decoder build up the same
  dictionary dynamically while receiving the data
• LZW places longer and longer repeated entries
  into a dictionary, and then emits the code for an
  element, rather than the string itself, if the
  element has already been placed in the dictionary

2
LZW compression for string ABABBABCABABBA

• The output codes are 1 2 4 5 2 3 4 6 1. Instead
  of sending 14 characters, only 9 codes need to be
  sent (compression ratio 14/9 1.56).

3
LZW decompression (1 2 4 5 2 3 4 6 1)
ABABBABCABABBA
4
LZW Coding (contd)

• In real applications, the code length l is kept
  in the range of l0, lmax. The dictionary
  initially has a size of 2l0. When it is filled
  up, the code length will be increased by 1 this
  is allowed to repeat until l lmax
• When lmax is reached and the dictionary is filled
  up, it needs to be flushed (as in Unix compress,
  or to have the LRU (least recently used) entries
  removed

5
7.6 Arithmetic Coding

• Arithmetic coding is a more modern coding method
  that usually out-performs Huffman coding
• Huffman coding assigns each symbol a codeword
  which has an integral bit length. Arithmetic
  coding can treat the whole message as one unit
• More details in the book

6
7.7 Lossless Image Compression

• Due to spatial redundancy in normal images I, the
  difference image d will have a narrower histogram
  and hence a smaller entropy

7
Lossless JPEG

• A special case of the JPEG image compression
• The Predictive method
• Forming a differential prediction A predictor
  combines the values of up to three neighboring
  pixels as the predicted value for the current
  pixel

8

• 2. Encoding The encoder compares the prediction
  with the actual pixel value at the position X
  and encodes the difference using Huffman coding

9
Performance generally poor, 2-3
10
Implementation details for VLC

• Consider the code for HELLO 10 110 0 0 111. how
  do you extract a bit? (decoding)
• union bitField
• struct
• unsigned int one1
• unsigned int two1
• unsigned int thr1
• unsigned int fou1
• unsigned int fiv1
• unsigned int six1
• unsigned int sev1
• unsigned int eig1
• bit
• unsigned char chr

Bit operators One (0xb1 0x80)gtgt7
11
Chapter 8 Lossless compression

• Information is permanently lost in the
  compression process to achieve higher compression
  ratios
• Metrics Mean square error, SNR, Peak SNR
• Primary loss mechanism quantization to reduce
  the number of different levels in the input
• Three different forms of quantization
• Uniform midrise and midtread quantizers
• Nonuniform companded quantizer (u-law, A-law)
• Vector Quantization

12
Transform coding

• The rationale behind transform coding
• If Y is the result of a linear transform T of the
  input vector X in such a way that the components
  of Y are much less correlated, then Y can be
  coded more efficiently than X
• If most information is accurately described by
  the first few components of a transformed vector,
  then the remaining components can be coarsely
  quantized, or even set to zero, with little
  signal distortion
• Discrete Cosine Transform (DCT)

13
Spatial Frequency and DCT

• Spatial frequency indicates how many times pixel
  values change across an image block
• The DCT formalizes this notion with a measure of
  how much the image contents change in
  correspondence to the number of cycles of a
  cosine wave per block
• The role of the DCT is to decompose the original
  signal into its DC and AC components the role of
  the IDCT is to reconstruct (re-compose) the signal

14
Graphical Illustration of 8 8 2D DCT basis
15
Chapter 9 Image compression

• JPEG standard - JPEG is a lossy image compression
  method. It employs a transform coding method
  using the DCT (Discrete Cosine Transform)
• An image is a function of i and j (or
  conventionally x and y) in the spatial domain.
  The 2D DCT is used as one step in JPEG in order
  to yield a frequency response which is a function
  F(u, v) in the spatial frequency domain, indexed
  by two integers u and v

16
Observations for JPEG Image Compression

• The effectiveness of the DCT transform coding
  method in JPEG relies on 3 major observations
• Observation 1 Useful image contents change
  relatively slowly across the image, i.e., it is
  unusual for intensity values to vary widely
  several times in a small area, for example,
  within an 88 image block.
• much of the information in an image is repeated
  (spatial redundancy)
• Observation 2 Psychophysical experiments suggest
  that humans are much less likely to notice the
  loss of very high spatial frequency components
  than the loss of lower frequency components
• spatial redundancy reduced by reducing the high
  spatial frequency contents
• Observation 3 Visual acuity (accuracy in
  distinguishing closely spaced lines) is much
  greater for gray (black and white) than for
  color
• chroma subsampling (420) is used in JPEG

17
JPEG encoder
18
DCT on image blocks

• Image is divided into 8 8 blocks. The 2D DCT is
  applied to each block image f(i, j), with output
  being the DCT coefficients F(u, v) for each block
• Using blocks, however, has the effect of
  isolating each block from its neighboring
  context. This is why JPEG images look choppy
  (blocky) when a high compression ratio is
  specified by the user

19
Quantization

• F(u, v) represents a DCT coefficient, Q(u, v) is
  a quantization matrix entry, and
  represents the quantized DCT coefficients which
  JPEG will use in the succeeding entropy coding
• quantization step is the main source for loss in
  JPEG
• The entries of Q(u, v) tend to have larger values
  towards the lower right corner. This aims to
  introduce more loss at the higher spatial
  frequencies a practice supported by
  Observations 1 and 2
• default Q(u, v) values obtained from
  psychophysical studies with the goal of
  maximizing the compression ratio while minimizing
  perceptual losses in JPEG images.

20

• The Luminance Quantization Table
• The Chrominance Quantization Table

16 11 10 16 24 40 51 61 12 12 14 19 26 58
60 55 14 13 16 24 40 57 69 56 14 17 22 29 51
87 80 62 18 22 37 56 68 109 103 77 24 35 55
64 81 104 113 92 49 64 78 87 103 121
120 101 72 92 95 98 112 100 103 99
17 18 24 47 99 99 99 99 18 21 26 66 99 99 99
99 24 26 56 99 99 99 99 99 47 66 99 99 99 99 99
99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99
99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99
21
515 65 -12 4 1 2 -8 5 -16 3 2 0 0 -11
-2 3 -12 6 11 -1 3 0 1 -2 -8 3 -4 2 -2
-3 -5 -2 0 -2 7 -5 4 0 -1 -4 0 -3 -1 0
4 1 -1 0 3 -2 -3 3 3 -1 -1 3 -2 5
-2 4 -2 2 -3 0 F(u, v)
22
(No Transcript)
23
Run-length Coding on AC coefficients

• To make it most likely to hit a long run of
  zeros a zig-zag scan is used to turn the 88
  matrix into a 64-vector

24
DPCM on DC coefficients

• The DC coefficients are coded separately from the
  AC ones. Differential Pulse Code modulation
  (DPCM) is the coding method
• If the DC coefficients for the first 5 image
  blocks are 150, 155, 149, 152, 144, then the DPCM
  would produce 150, 5, -6, 3, -8, assuming di
  DCi1 - DCi, and d0 DC0
• AC components are Huffman coded

25
Four Commonly Used JPEG Modes

• Sequential Mode the default JPEG mode, each
  graylevel image or color image component is
  encoded in a single left-to-right, top-to-bottom
  scan
• Progressive Mode
• Hierarchical Mode
• Lossless Mode discussed in Chapter 7

26
Progressive Mode

• Progressive JPEG delivers low quality versions of
  the image quickly, followed by higher quality
  passes
• Spectral selection Takes advantage of the
  spectral (spatial frequency spectrum)
  characteristics of the DCT coefficients higher
  AC components provide detail information
• Scan 1 Encode DC and first few AC components,
  e.g., AC1, AC2
• Scan 2 Encode a few more AC components, e.g.,
  AC3, AC4, AC5
• ...
• Scan k Encode the last few ACs, e.g., AC61,
  AC62, AC63.

27
Progressive Mode (Contd)

• 2. Successive approximation Instead of gradually
  encoding spectral bands, all DCT coefficients are
  encoded simultaneously but with their most
  significant bits (MSBs) first
• Scan 1 Encode the first few MSBs, e.g., Bits 7,
  6, 5, 4.
• Scan 2 Encode a few more less significant bits,
  e.g., Bit 3.
• ...
• Scan m Encode the least significant bit (LSB),
  Bit 0.